{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:07:10Z","timestamp":1790878030865,"version":"4.1.0"},"reference-count":59,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>\n                    Coexistence between cooperative and cheating individuals remains a central puzzle in social evolution. Here, we investigate how population density modulates coexistence using\n                    <jats:italic>Kluyveromyces lactis<\/jats:italic>\n                    strains that interact via physical attachment. Snowflake (cooperative) strains flocculate into multicellular clusters that settle efficiently, while Co-Uni (cheater) strains remain planktonic unless attached to Snowflakes, enabling them to exploit settling benefits without contributing to cluster formation. We manipulated settling density over 15 transfers (~60 generations) to alter encounter rates between strains while holding initial frequencies constant. At high densities, Co-Uni persistence was stabilized by frequent co-settling with Snowflakes; at low densities, reduced interaction frequency drove more rapid exclusion. Model-based projections revealed that both the rate of exclusion and the predicted equilibrium frequency of Co-Uni depend on settling density. Direct measurements of settling fitness confirmed that Co-Uni strains were less enriched in the settled fraction at low densities. These results demonstrate that interaction frequency, as modified by population density, can shape the ecological stability of social traits even in the absence of evolved enforcement or metabolic exchange. Our findings support the idea that density acts as a generalizable structural constraint on coexistence in microbial systems.\n                  <\/jats:p>","DOI":"10.1371\/journal.pone.0359779","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:35:56Z","timestamp":1790876156000},"page":"e0359779","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Population density constrains coexistence of cooperative and cheating Kluyveromyces lactis through frequency-dependent physical interactions"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4035-1521","authenticated-orcid":true,"given":"Rodrigo","family":"Zorrilla Gonz\u00e1lez","sequence":"first","affiliation":[{"name":"University of Minnesota","place":["St. Paul, Minnesota, United States of America"],"department":["Ecology, Evolution and Behavior"]},{"name":"Bravo Farms and 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Nadell","year":"2016","journal-title":"Nat Rev Microbiol"},{"issue":"4","key":"pone.0359779.ref003","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.1001547","article-title":"feedback between population and evolutionary dynamics determines the fate of social microbial populations","volume":"11","author":"A Sanchez","year":"2013","journal-title":"PLoS Biol"},{"issue":"1687","key":"pone.0359779.ref004","doi-asserted-by":"crossref","first-page":"20150090","DOI":"10.1098\/rstb.2015.0090","article-title":"Cheating and punishment in cooperative animal societies","volume":"371","author":"C Riehl","year":"2016","journal-title":"Philos Trans R Soc Lond B Biol Sci"},{"issue":"2","key":"pone.0359779.ref005","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.tim.2003.12.009","article-title":"Strategies of microbial cheater control","volume":"12","author":"M Travisano","year":"2004","journal-title":"Trends 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Resource supply and the evolution of public-goods cooperation in bacteria [cited 2025 Jul 25]. 2008. Available from: https:\/\/research-repository.st-andrews.ac.uk\/handle\/10023\/4636","DOI":"10.1186\/1741-7007-6-20"},{"issue":"1599","key":"pone.0359779.ref015","first-page":"2305","article-title":"The role of zooxanthellae in the thermal tolerance of corals: a \u201cnugget of hope\u201d for coral reefs in an era of climate change","volume":"273","author":"R Berkelmans","year":"2006","journal-title":"Proc Biol Sci"},{"key":"pone.0359779.ref016","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.ygeno.2014.10.004","article-title":"Experimental microbial evolution: history and conceptual underpinnings","volume":"104","author":"J Adams","year":"2014","journal-title":"Genomics"},{"issue":"8","key":"pone.0359779.ref017","doi-asserted-by":"crossref","DOI":"10.15252\/embr.201846992","article-title":"Microbial experimental evolution \u2013 a proving ground for evolutionary theory and a tool for discovery","volume":"20","author":"MJ McDonald","year":"2019","journal-title":"EMBO reports"},{"issue":"6","key":"pone.0359779.ref018","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.tree.2013.02.009","article-title":"Experimental coevolution of species interactions","volume":"28","author":"MA Brockhurst","year":"2013","journal-title":"Trends Ecol Evol"},{"issue":"7","key":"pone.0359779.ref019","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/S0966-842X(03)00152-5","article-title":"Social strife in the microbial world","volume":"11","author":"GJ Velicer","year":"2003","journal-title":"Trends Microbiol"},{"issue":"8","key":"pone.0359779.ref020","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1038\/nrmicro1461","article-title":"Social evolution theory for microorganisms","volume":"4","author":"SA West","year":"2006","journal-title":"Nat Rev Microbiol"},{"issue":"7244","key":"pone.0359779.ref021","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1038\/nature07921","article-title":"Snowdrift game dynamics and facultative cheating in yeast","volume":"459","author":"J Gore","year":"2009","journal-title":"Nature"},{"key":"pone.0359779.ref022","article-title":"The Prisoner\u2019s Dilemma and polymorphism in yeast SUC genes","author":"D Greig","year":"2004","journal-title":"Proc Biol Sci"},{"key":"pone.0359779.ref023","doi-asserted-by":"crossref","DOI":"10.7717\/peerj.17118","article-title":"In the social amoeba Dictyostelium discoideum, shortened stalks may limit obligate cheater success even when exploitable partners are available","volume":"12","author":"J Medina","year":"2024","journal-title":"PeerJ"},{"issue":"6815","key":"pone.0359779.ref024","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1038\/35050087","article-title":"Altruism and social cheating in the social amoeba Dictyostelium discoideum","volume":"408","author":"JE Strassmann","year":"2000","journal-title":"Nature"},{"issue":"6778","key":"pone.0359779.ref025","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1038\/35007066","article-title":"Developmental cheating in the social bacterium Myxococcus xanthus","volume":"404","author":"GJ Velicer","year":"2000","journal-title":"Nature"},{"key":"pone.0359779.ref026","doi-asserted-by":"crossref","first-page":"15707","DOI":"10.1038\/ncomms15707","article-title":"Synergistic cooperation promotes multicellular performance and unicellular free-rider persistence","volume":"8","author":"WW Driscoll","year":"2017","journal-title":"Nat Commun"},{"issue":"1","key":"pone.0359779.ref027","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1038\/s42003-024-06485-y","article-title":"Genomic sequencing reveals convergent adaptation during experimental evolution in two budding yeast species","volume":"7","author":"P Wang","year":"2024","journal-title":"Commun Biol"},{"issue":"2007","key":"pone.0359779.ref028","first-page":"20231055","article-title":"Multispecies interactions shape the transition to multicellularity","volume":"290","author":"M Kalambokidis","year":"2023","journal-title":"Proc Biol Sci"},{"issue":"45","key":"pone.0359779.ref029","article-title":"Genome duplication and mutations in ACE2 cause multicellular, fast-sedimenting phenotypes in evolved Saccharomyces cerevisiae","volume":"110","author":"B Oud","year":"2013","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pone.0359779.ref030","doi-asserted-by":"crossref","first-page":"6102","DOI":"10.1038\/ncomms7102","article-title":"Origins of multicellular evolvability in snowflake yeast","volume":"6","author":"WC Ratcliff","year":"2015","journal-title":"Nat Commun"},{"issue":"1976","key":"pone.0359779.ref031","first-page":"20212722","article-title":"Loss-of-heterozygosity facilitates a fitness valley crossing in experimentally evolved multicellular yeast","volume":"289","author":"B Baselga-Cervera","year":"2022","journal-title":"Proc Biol Sci"},{"key":"pone.0359779.ref032","unstructured":"R Core Team. R: The R Project for Statistical Computing. 2024 [cited 2024 Sep 16]. Vienna, Austria. Available from: https:\/\/www.r-project.org\/"},{"key":"pone.0359779.ref033","unstructured":"Bates D, Maechler M, Bolker B, Walker S, Christensen RHB, et al. lme4: Linear Mixed-Effects Models using \u201cEigen\u201d and S4. 2024 [cited 2024 Sep 16]. Available from: https:\/\/cran.r-project.org\/web\/packages\/lme4\/index.html"},{"key":"pone.0359779.ref034","unstructured":"Sprouffske K. Growthcurver: Simple metrics to summarize growth curves. 2020 [cited 2024 Sep 16]. Available from: https:\/\/cran.r-project.org\/web\/packages\/growthcurver\/index.html"},{"key":"pone.0359779.ref035","unstructured":"Wickham H, RStudio. Tidyverse: Easily install and load the \u201ctidyverse\u201d. 2023 [cited 2024 September 16]. Available from: https:\/\/cran.r-project.org\/web\/packages\/tidyverse\/index.html"},{"key":"pone.0359779.ref036","unstructured":"Robinson D, Hayes A, Couch S. broom: Convert Statistical Objects into Tidy Tibbles. 2024 [cited 2024 September 16]. Available from: https:\/\/cran.r-project.org\/web\/packages\/broom\/index.html"},{"key":"pone.0359779.ref037","unstructured":"Bolker B, Robinson D, Menne D, Gabry J, Buerkner P. broom.mixed: Tidying Methods for Mixed Models. 2024 [cited 2024 September 16]. 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Frenkel","year":"2015","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"6688","key":"pone.0359779.ref041","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1038\/27900","article-title":"Adaptive radiation in a heterogeneous environment","volume":"394","author":"PB Rainey","year":"1998","journal-title":"Nature"},{"issue":"19","key":"pone.0359779.ref042","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1016\/j.cub.2012.08.005","article-title":"Competition, not cooperation, dominates interactions among culturable microbial species","volume":"22","author":"KR Foster","year":"2012","journal-title":"Curr Biol"},{"issue":"5","key":"pone.0359779.ref043","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1073\/pnas.1115323109","article-title":"Experimental evolution of multicellularity","volume":"109","author":"WC Ratcliff","year":"2012","journal-title":"Proc Natl Acad Sci U S 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Microbiol"},{"issue":"2","key":"pone.0359779.ref047","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.tim.2013.12.004","article-title":"Interactions in multispecies biofilms: do they actually matter?","volume":"22","author":"M Burm\u00f8lle","year":"2014","journal-title":"Trends in Microbiology"},{"issue":"9","key":"pone.0359779.ref048","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1038\/nrmicro.2016.94","article-title":"Biofilms: an emergent form of bacterial life","volume":"14","author":"H-C Flemming","year":"2016","journal-title":"Nat Rev Microbiol"},{"issue":"3","key":"pone.0359779.ref049","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1080\/1040841X.2021.1887079","article-title":"Community-wide changes reflecting bacterial interspecific interactions in multispecies biofilms","volume":"47","author":"FA Sadiq","year":"2021","journal-title":"Crit Rev Microbiol"},{"issue":"6107","key":"pone.0359779.ref050","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1126\/science.1208929","article-title":"Marine microbes see a sea of gradients","volume":"338","author":"R Stocker","year":"2012","journal-title":"Science"},{"issue":"23","key":"pone.0359779.ref051","doi-asserted-by":"crossref","DOI":"10.1002\/adfm.202110699","article-title":"Mechanical Resilience of Biofilms toward Environmental Perturbations Mediated by Extracellular Matrix","volume":"32","author":"Q Zhang","year":"2022","journal-title":"Adv Funct Materials"},{"key":"pone.0359779.ref052","article-title":"Myxobacteria: Moving, Killing, Feeding, and Surviving Together","author":"J Mu\u00f1oz-Dorado","year":"2016","journal-title":"Front Microbiol"},{"issue":"19","key":"pone.0359779.ref053","doi-asserted-by":"crossref","first-page":"3805","DOI":"10.1016\/j.jmb.2016.07.008","article-title":"Molecular Mechanisms of Signaling in Myxococcus xanthus Development","volume":"428","author":"DJ Bretl","year":"2016","journal-title":"J Mol Biol"},{"issue":"1","key":"pone.0359779.ref054","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1242\/jcs.19.1.215","article-title":"Cell density dependence of the aggregation characteristics of the cellular slime mould Dictyostelium discoideum","volume":"19","author":"Y Hashimoto","year":"1975","journal-title":"J Cell Sci"},{"issue":"3","key":"pone.0359779.ref055","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1093\/evolut\/qpac038","article-title":"From individual behaviors to collective outcomes: fruiting body formation inDictyosteliumas a group-level phenotype","volume":"77","author":"JJ Kuzdzal-Fick","year":"2022","journal-title":"Evolution"},{"key":"pone.0359779.ref056","doi-asserted-by":"crossref","unstructured":"Estrela S, Diaz-Colunga J, Vila JCC, Sanchez-Gorostiaga A, Sanchez A. Diversity begets diversity under microbial niche construction. bioRxiv. 2022. 2022.02.13.480281. https:\/\/www.biorxiv.org\/content\/10.1101\/2022.02.13.480281v1","DOI":"10.1101\/2022.02.13.480281"},{"issue":"49","key":"pone.0359779.ref057","article-title":"An oligotrophic deep-subsurface community dependent on syntrophy is dominated by sulfur-driven autotrophic denitrifiers","volume":"113","author":"MCY Lau","year":"2016","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pone.0359779.ref058","article-title":"Disentangling a metabolic cross-feeding in a halophilic archaea-bacteria consortium","author":"NO Medina-Ch\u00e1vez","year":"2023","journal-title":"Front Microbiol"},{"issue":"2","key":"pone.0359779.ref059","doi-asserted-by":"crossref","DOI":"10.1128\/mBio.00036-12","article-title":"The Black Queen Hypothesis: Evolution of Dependencies through Adaptive Gene Loss","volume":"3","author":"JJ Morris","year":"2012","journal-title":"mBio"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0359779","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:36:05Z","timestamp":1790876165000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0359779"}},"subtitle":[],"editor":[{"given":"Satheesh","family":"Sathianeson","sequence":"first","affiliation":[{"name":"King Abdulaziz University","place":["SAUDI ARABIA"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":59,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0359779","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,1]]}}}